The book of Galatians is short (only 6 chapters) and Paul doesn't have time to be subtle. So, after brief, perfunctory greetings, he gets right to the point:
What the heck is wrong with them?????
Why are they abandoning the gospel he preached to them?
That's what he has been hearing. Since Paul has left the church in Galatia, others have come, and they have been telling the Galatians that trust in Jesus' death and resurrection is not enough to be considered a follower of Jesus. They also need to be circumcized, and keep the law. This Paul emphatically rejects. And he is angry that it is so easy for them to desert the gospel and cling, instead, to the law.
These false teachers are often called "Judaizers." While Paul is careful not to tell the Galatians that the law is bad, he wants them to know that the law does not save them. Paul tells the Galatians that the other apostles agreed with him on this (including Peter, who is called "Cephas" in this letter), and he feels that they were cowardly and hypocritical to cave in when opposition hit.
Paul is not going to do this. He tells the Galatians a little of his own history, about how he, a zealous Pharisee, came to believe in Jesus, and how he came to be an apostle to the Gentiles. He gives a short, passionate synopsis of his theology from Romans: The righteous will live by their faith. And the covenant with Abraham, based on Abraham's trust, takes precedence over the covenant based on the law. In fact, the covenant that is based on the giving of the law actually depends on the covenant God gave with Abraham.
Do you ever wonder: why is Paul so passionate about this? What's the big deal? What is he afraid of? What is the slippery slope here?
Perhaps, as we complete the letter tomorrow, we'll get some ideas.